decision-focused learning

This work systematically investigates decision-focused learning (DFL) in the context of stochastic linear programming, revealing that under the conventional “predict-then-optimize” paradigm, improved prediction accuracy does not necessarily translate into better downstream decision quality. The study demonstrates fundamental limitations of standard statistical learning approaches and common data collection strategies—along with distributional metrics such as Wasserstein distance—when applied to optimization tasks. By developing a unified framework that jointly models prediction and optimization, the paper clarifies the essential differences between DFL and traditional predictive modeling. Building on these insights, it proposes novel methods explicitly designed to optimize decision performance, thereby laying foundational groundwork for theory and tools in decision-oriented machine learning.

Two-stage prediction-decision frameworks suffer from instability under decision uncertainty—PFL ignores decision quality, while DFL optimizes decisions but exhibits poor convergence. Method: We propose an end-to-end decision-oriented learning framework that jointly integrates prediction and decision losses via gradient fusion: prediction gradients guide decision optimization, enhancing decision quality without compromising training stability; we further introduce a sigmoid-decaying gradient perturbation strategy embedded within a differentiable optimization framework, ensuring compatibility with diverse DFL solvers. Contribution/Results: We provide theoretical convergence guarantees without requiring auxiliary training. Empirical evaluation across three stochastic optimization tasks demonstrates significant reduction in decision regret, improved training stability, and robust superior performance—even in regimes where conventional methods fail.

In scientific computing applications—such as trajectory prediction, optimal control, and minimum energy path computation—downstream algorithms critically depend on accurate model evaluations. Conventional mean-squared-error-based supervised learning often induces task-specific performance degradation due to misalignment between the loss function and the ultimate algorithmic objective. Method: We propose a task-oriented predictive modeling paradigm that replaces standard regression losses with a surrogate objective: the maximum prediction error over a downstream task support set. Our framework integrates sampling measure modeling, empirical risk discretization, and iterative optimization to directly optimize downstream algorithmic performance. Contribution/Results: This is the first approach to explicitly embed downstream robustness requirements into the training objective. Evaluated across multiple scientific computing benchmarks, it consistently improves both predictive accuracy and algorithmic stability, demonstrating superior generalization under task-relevant perturbations.

In modern port electric logistics scheduling, the dynamic arrival of vessels undermines the generalizability and task adaptability of conventional prediction-optimization paradigms. Method: This paper proposes a decision-oriented continual learning framework that jointly integrates Fisher information matrix regularization with a differentiable convex surrogate optimization model. The framework enables end-to-end co-optimization of prediction and scheduling decisions, ensuring memory stability over historical tasks while supporting online adaptation to newly arriving vessel streams. Contribution/Results: Compared to existing decision-oriented learning approaches, our method significantly improves cross-task generalization and decision quality while reducing long-term computational overhead. Empirical evaluation on real-world operations at Jurong Port demonstrates superior scheduling performance over state-of-the-art methods, validating both its theoretical innovation and engineering practicality.

Many real-world decision-making problems exhibit multi-stage structures, temporal dependencies, and intertemporal effects—characteristics inadequately addressed by prevailing decision-focused learning methods, which predominantly assume single-stage settings. To bridge this gap, we propose the first decision-oriented predictive framework explicitly designed for multi-stage optimization: it jointly trains predictive models and dynamic decision policies in an end-to-end differentiable manner, explicitly encoding temporal decision dependencies via differentiable optimization. Furthermore, we introduce an implicit multi-layer recurrent architecture that captures feedback from state trajectories to predictions, and theoretically establish its gradient-based self-correcting mechanism for prediction bias. Evaluated on an energy storage arbitrage task, our method substantially outperforms both decoupled predict-then-optimize baselines and single-stage counterparts, achieving a 12.7% improvement in long-horizon cumulative reward.

This work addresses the scalability challenge in predict-then-optimize paradigms, where directly minimizing decision regret is hindered by the almost-everywhere non-differentiability of the optimization mapping and reliance on costly solvers. The authors propose a novel training method that eliminates solver calls during learning by designing a surrogate loss grounded in measure transport theory. This approach enables fully solver-free, decision-focused learning while preserving theoretical guarantees—including Fisher consistency and excess risk bounds—and achieves comparable decision performance to state-of-the-art methods. Notably, it reduces training time by several orders of magnitude, marking the first solver-independent framework for predict-then-optimize with both scalability and rigorous theoretical foundations.

This study addresses decision failures caused by predictive overfitting in contextual optimization by proposing a decision-driven regularized bi-objective framework. The method employs surrogate functions to resolve cost ambiguity, effectively balancing prediction accuracy with decision costs while unifying robust optimization and regret minimization perspectives and generalizing models such as SPO+. Experimental results on synthetic datasets demonstrate that the proposed framework significantly outperforms baselines including OLS, XGBoost, and SPO+, thereby enhancing both robustness and economic efficiency in end-to-end decision-making. Ultimately, this work establishes a novel paradigm for the synergistic integration of prediction and optimization.

This work addresses the high computational cost or objective bias in traditional decision-focused learning, where regret gradients rely on differentiable solvers or surrogate losses. The authors propose Projected Error as Regret Gradient (PEAR), a method that derives a closed-form geometric expression for regret gradients by projecting prediction errors onto the tangent space of active constraints and incorporating local curvature—eliminating the need for iterative solving or auxiliary optimization. PEAR constructs a reduced-dimensional linear system based on the active constraint set to enable efficient gradient computation. Experiments demonstrate that PEAR significantly outperforms existing baselines on both linear programming and real-world quadratic programming tasks, achieving superior performance in decision quality, computational efficiency, and robustness under varying constraints.

Traditional feature importance methods struggle to interpret combinatorial investment decisions where prediction and optimization are tightly coupled, and they fail to elucidate how macroeconomic conditions influence investment outcomes. This work proposes a novel prediction–optimization–explanation framework that, for the first time, integrates gradient-guided counterfactual sample generation with portfolio optimization to construct economically meaningful “what-if” scenarios. By jointly modeling the prediction and optimization processes, the method flexibly generates macroeconomic scenarios tailored to specific investment objectives, effectively identifying critical conditions—such as those that narrow strategy return gaps, trigger diversification, or enable excess returns. Empirical results demonstrate that the proposed framework substantially enhances both the interpretability and robustness of portfolio strategies.

This work addresses the inefficiency of traditional sequential experimental design in the predict-then-optimize paradigm, which stems from its neglect of downstream decision loss. The authors propose a decision-oriented sequential design method that directly optimizes the performance of downstream linear optimization problems by introducing a novel measure of directional uncertainty that does not require an optimization oracle. Unlike conventional approaches that prioritize predictive accuracy alone, this method targets decision quality while maintaining computational efficiency and enjoying strong consistency and convergence guarantees. Theoretical analysis demonstrates that the approach achieves earlier stopping times under broad distributional assumptions. Empirical evaluation on a real-world task allocation problem involving large language models shows significant improvements over existing methods.